Complex Number Calculator
Calculate complex arithmetic, powers and principal natural logarithms in a + bi form.
Formula
i²=−1; (a+bi)(c+di)=(ac−bd)+(ad+bc)i; Log z=ln|z|+i Arg z; zʷ=exp(w Log z).
Real part ≈ (3)+(2) · Imaginary coefficient ≈ (-4)+(5)
How to use
- Enter a,b for z₁ and c,d for z₂.
- Choose an operation; Log uses z₁ only.
- Read the real part and imaginary coefficient.
Examples
- (3−4i)+(2+5i)=5+i.
Frequently asked questions
Which logarithm and power branch is used?
The principal branch, −π<Arg z≤π. Other logarithm values differ by 2πki.
When is zero excluded?
The divisor must be nonzero. Log and power require a nonzero base; power uses exp(z₂ Log z₁).
Where is polar form?
Use the related polar-form converter for modulus and argument.
Sources
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